Comparative study of afterpulsing behavior

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by  Abdul W. Ziarkash

Comparative study of afterpulsing behavior
Abdul W. Ziarkash,1 Siddarth Koduru Joshi,2,a) Mario Stipˇcevi´c,3 and Rupert Ursin4,b)
1)Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences Vienna A-1090
2)Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences,
Vienna A-1090
3)Ruder Boskovic Institute, Center of Excellence for Advanced Materials and Sensors and Division of Experimental
Physics, Zagreb 10000, Croatia
4)Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences,
Vienna A-1090
Vienna Center for Quantum Science and Technology (VCQ).
(Dated: 17 January 2017)
7 PACS numbers: 03.67.Dd, 03.67.Hk, 85.60.Gz, 06.20.fb, 07.60.-j, 87.64.-t,
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Keywords: Afterpulse, Avalanche photodiode, APD, Single photon detection
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n Single-photon detectors, like Avalanche Photo Avalanche Photo Diodes (APDs) operated above their
a Diodes (APDs), have a great importance in many breakdown voltage in Geiger mode. Such as in photon-
J
fields like quantum key distribution, laser rang- ics quantum processing tasks, laser ranging, fluorescence

2 ing, florescence microscopy, etc. Afterpulsing is a microscopy, neural imaging with blood flow tomography,
1
typical non ideal behavior of APDs, operated in contrast-enhanced MRI, two-photon luminescence imag-

Geiger mode, which adversely affects any appli- ing, astronomical telescopes, etc.5,6,11,12,19,26,28. They
]
t cation which measures the number or timing of arewidelymanufacturedandsoldbymanydifferentcom-
e
d detection events. Several conflicting studies have panies and as such exhibit different properties/behavior.
- triedtomodelafterpulsingbehaviorandlinkitto To efficiently and accurately perform these experiments
s fundamental semiconductor physics3,7,8,13,15,17,25. we must account for all non-ideal behavior of the detec-
n
i Here we describe experiments we performed on tors used1,4. This is especially true for sensitive applica-
.
s at least 2 different detectors from 3 manufac- tions like quantum communication, because the security
c turers, all commonly used in quantum optics se- ofanyrealworldimplementation(i.e. withahightrans-
i
s tups. We report on the timing structure of the missionloss)dependsonthedevicesused. Hencethepre-
y counts. By fitting different models to these data, cise modeling/characterization of the non ideal behavior
h
we found statistically significant differences be- of single photon detectors (and all other components of
p
tween the detectors used. Furthermore, we re- thequantumcommunicationdevice)arecriticalforprac-
[
port on the presence of high order afterpulses tical security proofs.

1 whicharenotaccountedforinanyofthestandard Anidealsingle-photondetectorgeneratesoneandonly
v
models of afterpulse behavior. This might have one electric pulse for every incident photon. However, in
3
8 significant implication e.g. in quantum key distri- a real detector, it is possible that a single incident pho-
7 bution systems, as the modeling of the devices in ton results in more than one electrical pulse per incident
3 usewillhavetobepartofthesecurityanalysisfor photon. This is known as afterpulsing.1 In this work we
0 some systems9,10. Significant differences between definean“afterpulse”asanypulseinadditiontoandfol-
1. manufacturers and even between seemingly iden- lowingthedetectioneventcausedbyanincidentphoton,
0 tical detectors of the same make and batch sug- regardless of its etiology. This behavior has been ex-
7 gest that every individual detector needs to be tensivelystudiedduetoitsimportanceinsemiconductor
1 calibrated. We describe a reliable procedure to physics in general. It has been suggested that afterpuls-
v: perform such a calibration and present our find- ing can be linked to charges trapped in the deep levels
i ings on three different commercial products. of the semiconductor’s band structure and released at
X
a later time3 as well as to an artifact of the electronics
r like unsuccessful quenching2 or twilighting22,24,29 (i.e. a
a
detection event towards the end of the dead time).
I. INTRODUCTION
Afterpulsing has different implications, depending on
the application of the detector used. It can result in
Applications of single-photon detectors, which focus an overestimation of the total count rate by up to 10%
on the timing of a very weak optical signal, mostly use as well as a reduction of the duty cycle and detection
efficiency due to the increased dead times. In fluores-
cence microscopy it could lead to an overestimation of
the concentration of fluorophores. In quantum commu-
a)Electronicmail: [e-mail]. nication the overestimation of coincidence events leads
b)Electronicmail: [e-mail]. to larger Quantum Bit Error Ratio (QBER). Afterpuls-
2
ing can also adversely affect security16 and hence part is given by:
of the security analysis of the quantum key distribution
system. Afterpulsing poses also a significant problem to P (t)=2·A· sinh(∆·t) ·e−γ·t+d, (3)
the measurement of photon arrival times both in quan- sinc t
tum communication protocols as well as for laser rang-
where ∆ and γ are both functions of the minimum and
ing. Hence a proper characterization of the afterpulse
maximum energies of the deep levels in which charges
behaviour could improve the accuracy of several mea-
may be trapped.
surements in meterology in general. Further, studying
In this paper, we compare the above three standard
the afterpulses could lead to a better understanding of
mathematical models (see Equations 1, 2 and 3) with
the underlying mechanism within the semiconductor.
the measured behavior of several different single pho-
Severalpreviousworkshaveattemptedtocharacterize
ton counting APDs (SPCM-AQ4C from PerkinElmer,
theafterpulsebehaviorandfittheresultstovariousmod-
SPCM-NIR from Excelitas and τ-SPAD-fast from Laser
els3,7,8,13,15,17,25. Worryingly, these papers do not agree
Components). We show that none of these canonical
on the most suitable model describing the statistics of
models are universal and vary between makes of detec-
the arrival times. All these studies have focused on one
tors. We also report on the presence of several higher
make/manufacture of detector at a time. In this work
order afterpulses. An investigation of the region of re-
we take a more comprehensive approach and perform
duced detection efficiency called the “dead-time” found
a comparative study on 3 different makes of APDs (for
betweenthesignalpulseandtheafterpulseshowsyetan-
eachmakewecompare2individualdetectorswithalmost
othercharacteristicvariationbetweenmakesofdetectors,
consecutive serial numbers). We test the universality of
which is not part of the models used so far.
thevarioustheoreticalmodelsandattempttoresolvethe
conflicts raised by these works. To do so we eschew the
commonpracticeofstudyingthetimingauto-correlation
II. EXPERIMENTAL SETUP
of the APD signals in favor of the more comprehensive
timingcross-correlationbetweentheemissionofaphoton
and all the following APD signals. We describe this pro-
cedure in Section II. We then fit to the various standard Function Pc
Generator
models described below and compare these fits in Sec-
tion IIIA. Due to our use of cross-correlations we were
also able to detect higher orders of afterpulses which we
present in Section IIIB and finally in Section IIIC we Pulsed LED ND Time Tagging
Laser Filter Detector Module
discuss the corrections that can be applied.
The characteristic decay of the afterpulse probability
was sometimes thought to depend on the deep level in
for controlled μ = 0.1
which the charge is trapped. Initial models3,7,8,18,30 con- 1 ns pulse, background photons/pulse
0.25 - 1 MHz
sidered the decay from several distinct deep levels and
proposedthe“multipleexponentialmodel”wheretheaf- FIG. 1: A 798nm laser is used to generate pulses with a
terpulsing probability (P (t)) at a time t is given by: 1ns pulse width and various repetition rates between
exp
0.25 to 1MHz. We use Neutral Density (ND) filters to
Pexp(t)=(cid:88)Ake−τtk +d, (1) attenuate the laser pulse, incident on the active area of
the APDs, until we have (cid:28) 1 detected photon per laser
k
pulse (approximately corresponding to a mean photon
where τk and Ak is the de-trapping lifetime and ampli- number of 0.1 per pulse). We use a time tagging
tude factor for the kth deep level, and d is the offset due module (TTM8000) with a resolution of 82.3ps to
to noise counts. record the trigger for the laser pulse (Channel 1) and
Furthermore14,15 considered a continuum of deep lev- the photon detection event (Channel 2). This data is
els,inInGaAsandInPdetectors,thatcouldtrapacharge stored on a computer and a software computes the
andfoundthatthe“powerlaw”wasagoodempiricalfit. temporal cross-correlation histogram (g(2)) with 1ns bin
Here the afterpulse probability (Ppow(t)) is given by: width. The LED shown was only used to obtain the
results shown in Section IIIC.
P (t)=A·t−λ+d, (2)
pow
The general scheme of the setup used for the experi-
where λ is a effective decay constant and A is the the mentsisshowninFigure1. Afunction-generatortriggers
initial afterpulse probability. a 789 nm laser with a repetition rate of 0.25 to 1MHz
In an another attempt to create a more physically kHz. Theemittedlightpulseof≈1nslengthgetsatten-
meaningfulmodel13 derivedthe“hyperbolicSincmodel” uated in a neutral attenuator to <0.1 photons per pulse
from the Arrhenius law (once more assuming a contin- on average and arrives at the active area of the respec-
uumoflevels),wheretheafterpulseprobability(P (t)) tivedetectorinuse. Thearrivaltimeatthedetectorand
sinc
3
the trigger from the function generator are individually On the whole, the power model had the most consis-
sent to a time-tagging-module (TTM). We then calcu- tent good fit and the hyperbolic Sinc model the worst.
lated the temporal cross-correlation histogram (g(2)) be- Unlike the hyperbolic Sinc model, the power model ap-
tweenthosetwosignalsusingabinwidthof1ns. Wenor- proximates the experimental data more accurately inde-
malize to the number of laser pulses to obtain the pulse pendent of the APD used (AQ4C, SPCM-NIR, τ-SPAD-
probability per bin and integrate over the entire peak to fast). 13 showed that the hyperbolic sinc model was bet-
obtain the total pulse probability. To ensure that our terthanthepowermodelusingid100-MMF50APDmod-
resultsarenotskewedbyanindividual“faulty”detector ule from idQuantique, we were unable to duplicate those
we tested at least 2 detectors of each type (same man- results with any of our detectors.
ufacturer’s model number with nearly consecutive serial
numbers) all of similar ages. One can clearly see in Figure 2 that the Power model
WeconsiderthefirsteventarrivingattheTTM,aftera is fitting the entire range of the tail better than the Hy-
givenlaserpulsetobethe”detectionpulse”whichstems perbolic sinc model. The goodness of the fits can be
from the real photon impinging on the active area of the quantitatively compared using the residuals seen in Fig-
detector. Any detection event after that, but before the ure 2 which are well within the ± 2 standard deviation
nextlaserpulse,shouldbeduetotoeitherafterpulsingor range(showninred)forthepowermodelbutnotforthe
noise. Consequently, we do not differentiate between an hyperbolic sinc model.
afterpulse due to processes in the semiconductor diode
from those due to secondary avalanches caused by the Powermodelasasimpleanalyticmodelfunctionleads
quenching circuit. This is typical of most applications to some good results (as seen in Figure 2). The power
of these detectors ranging from (quantum) optics exper- model was primarily shown to be effective for InGaAS
iments to fluorescence microscopy. and InP detectors14,15,23 and we now show that it is a
Wefiteachofthestandardmodels(seeEquations1,2 reasonablygoodmodelforthedifferenttypesofSidetec-
and Equation 3) to the tail of the afterpulse as seen in tors we tested. However, it’s estimated parameters gives
the g(2) obtained for each different APD. Figure 2 shows a rather loose description of the physical origin of after-
the resultant fits as well as the residuals. pulses. Atrulygoodmodelshouldbeabletopredictthe
All current models of afterpulsing discussed, concern behavior of the entire tail region. The power model only
thetimingstructureoftheafterpulsetail. Anidealmodel provides a suitable fit if the beginning of the afterpulse
ofadetectorshouldincludeitsentirebehaviourincluding tail is ignored. Further,13 showed that this model was
the duration of the dead time, the jitter and the rising not suitable for his idQuantique id100-MMF50 modules.
edge of the afterpulse peak. As in all previous publica-
The multiple exponential model provides a good fit
tions mentioned above, we then isolate the peak (due to
when k (cid:62) 5 and is slightly better than the power model
afterpulses)anditstailintime. Thetailoftheafterpulse
for the SPCM-AQ4C detector. It is nearly commen-
ofallAPDsareshowninFigure2afternormalizationand
surate with the power model for the τ-SPAD. For the
accidentals correction have been applied (as discussed in
SPCM-NIR, the exponential model gives a good fit only
Section IIIC). We define the total afterpulse probabil-
when we ignore the higher order afterpulse peaks (which
ity to be the sum total of the afterpulse probability in
each bin of the corrected g(2) histogram for a duration are discussed in Section IIIB). We observed that it was
of 900ns31. Regardless of the model, in order to obtain possible to get different fits of almost the same quality
with different characteristic times (τ also called the de-
a good fit we had to ignore the first two points of the k
trapping times) depending on the number of exponen-
afterpulse tail.
tials used. Thus, upon examining the fitting procedure
we concur with15 who state that “It is evident from this
whole fitting procedure that the extracted values for the
III. RESULTS
de-trapping times depend entirely on number of expo-
nentials in the model function and the range of hold-off
A. Comparison of afterpulsing models
times used in the data set.”
We observed a wide variation between different de- In case of the hyperbolic sinc model, we consistently
tectors. We tested 2 to 3 identical (in terms of make, obtainunsuitablefitstoourexperimentaldata. However,
modelnumberandyearofpurchase)detectorsfromeach the behavior of detectors from other manufacturers may
of three manufacturers. We saw a drastic change in the be better described by this model13.
total afterpulse probability between otherwise identical
detectors. The total afterpulse probability of τ-SPAD- Afterpulse behavior and probabilities vary drastically
fast with serial number 01019917 was 5.1± 0.003% and betweenbrands(asseeninFigure3). Thetotalprobabil-
that with serial number 01019920 was 8.5± 0.002% (see ity of obtaining an afterpulse (P(AP)) for each detector
Table I). However, each identical detectors, had nearly is shown in Table I. In addition, the same table shows
the same fitting parameters for the same model. The the time taken for the fit of the afterpulse probability to
only significant difference was the amplitude factor A. fall to 10% (τ ) and 15% (τ ).
10% 15%
4
1×10-4 10
Data Data
Power Law Power Law
Sinhc Law Sinhc Law
8×10-5 4×10-5 Multi exp. Law 5 Multiple exp. Law
ability6×10-5 -6×10
ulse prob4×10-5 2×10-5 esiduals 0
P 0×100 R
0 20 40 60 80 100 -5
2×10-5
0×100 -10
0 100 200 300 400 500 0 50 100 150 200 250 300 350 400
Δt (ns) Time (ns)
(a) SPCM-AQ4C (b) SPCM-AQ4C
8×10-4 15
Data Data
Power Law Power Law
Sinhc Law 10 Sinhc Law
Multi exp. Law Multi exp. Law
6×10-4 2×10-4
bility -610 5
a ×
e prob4×10-4 1×10-4 22ns 22ns 22ns duals 0
uls esi-5
P 0×100 R
2×10-4 0 20 40 60 80 100
-10
0×100 -15
0 100 200 300 400 500 0 50 100 150 200 250 300 350 400
Δt (ns) Time (ns)
(c) SPCM-NIR (d) SPCM-NIR
8×10-4 Data 20 Data
PSoinwhecr LLaaww 15 PSoinwhecr LLaaww
Multi exp. Law Multi exp. Law
6×10-4 2×10-4 10
y
bilit 5
a
prob4×10-4 1×10-4 0
se -5
ul
P 0×100
2×10-4 40 80 120 160 200 240 280 -10
-15
0×1000 100 200 300 400 500 -200 50 100 150 200 250 300 350 400
Δt(ns) Time (ns)
(e) τ-SPAD-fast (f) τ-SPAD-fast
FIG. 2: Afterpulse peak’s tail fitted with Power model, Hyperbolic-sinc model and multiple exponential model for
SPCM-AQ4C (PerkinElmer), SPCM-NIR (Excelitas) and τ-SPAD-fast (Laser Components) - Comparison of
residuals for all detectors and models (Power model (blue), Hyperbolic sinc model (cyan) and Multiple exponential
model (green)) and the red dashed lines are ± 2 standard deviation limits for statistical fluctuations. We analysed
>0.14×106,2.7×106 and 3×106 afterpulse events for each SPCM-AQ4C, SPCM-NIR, and τ-SPAD-fast detector
we analysed respectively.
B. Higher order afterpulses enough twilighting22, photon detections and afterpulses
accumulate in a narrow peak that appear just after the
deadtime. WenotethisbehaviorinSPCM-NIRandtoa
Any detection event may cause an afterpulse which
lesserextentinSPCM-AQ4C,ascanbeseeninFigure3.
may induce secondary and further afterpulses which we
Thehigherorderafterpulsesareclearlyvisibleasaseries
call “higher order afterpulses”. Usually afterpulsing is
of peaks after the main peak with a period exactly equal
a small effect and the afterpulsing probability distribu-
to the dead time of the detector. The presence of such
tionfunctionissmearedsuchthatthehigherorderafter-
higherorderafterpulsingwasfirstspeculatedin15 but,to
pulsesareimprobable. However,inthepresenceofstrong
5
Detector P(AP) (%) τ10% (ns) τ15% (ns) tdead (ns) bilityofanafterpulseinthebinjustbeforethenthhigher
SPCM-AQ4C 0.2854±0.0008 7 3 50 order peak × the number of bins in the peak. This geo-
SPCM-NIR 1.2904±0.0007 8 6 22 metric progression agrees to within 4 to 6% for the 2nd
τ-SPAD-fast 5.106±0.003 119 80 53 to 5th order afterpulses.
TABLE I: Table showing the total afterpulse
probability (P(AP)), the decay time of the afterpulse to
10% (15%) of maximum — τ (τ ) and the dead C. Background and accidentals corrections during the
10% 15%
time (t ) of each of the detector makes. dead time
dead
SPCM-AQ4C Sn. 195 (2007), SPCM-NIR Sn. 29860
(2015) and τ-SPAD-fast Sn. 01019917 (2013)
An investigation of the region of reduced detection ef-
ficiency called the “dead-time” found between the signal
pulseandtheafterpulseshowsyetanothercharacteristic
the best of our knowledge, never reported. variation between makes of detectors, which is not part
FortheSPCM-NIR,thesignalpulseandthefirstorder of the models used so far. In typical quantum optics
of afterpulse are 22ns apart, which exactly corresponds experiments, there is a probability that a coincidence is
to the duration of the dead time of this particular de- detected between two different detectors erroneously, we
tector module. The measured time intervals between all callthesecoincidences“accidentals”. Typically,theycan
followinghigherordersofafterpulses(asseenintheinset beestimatedfromPoissonianstatisticsas: r =r r t ,
acc 1 2 c
of the Figure 3) have the same time delay of 22ns. We where r is the rate of the accidental counts, r and
acc 1
have obtained a similar plot for three detectors with the r are the count rates of the individual detectors and t
2 c
same model number: in each case, peaks appear sepa- is the coincidence time window used. In the duration
ratedbythedeadtimeoftheparticulardetector. Sucha well after a detection event, this provides a very good
behavior is clearly undesirable, notably in time-resolved estimate (with a maximum variation of (cid:28) 3%) of the
spectroscopywherehigherorderpeakscouldbemistaken behavior. However, shortly after the detection event the
for, or mask the true signal. detectorsexhibita“deadtime”andthismaybefollowed
by an afterpulse. Many experiments simply subtract the
accidental counts and this may be a good approxima-
SPCM-NIR (Excelitas)
SPCM-AQ4C (PerkinElmar) tion when the detection rates are very low compared to
100 22ns 22ns τ-SPAD-fast (Laser Components) the peak count rate. At high detection rates, the effect
22ns
22ns 22ns of afterpulses and the dead time become significant. In
bility10-2 10-4 theprevioussectionswehavecharacterizedtheafterpulse
a
b probabilityforseveraldetectors. Inthissectionwefocus
o
e pr10-4 10-6 0 20 40 60 80 100 on the effect of the dead time.
s
ul “Deadtime”isamisnomerbecausethedetectorisnot
P
10-6 completely dead/inactive instead it exhibits a reduced
detectionefficiency. Wefindthatthedetectionefficiency
is reduced by a factor α which is characteristic of the
10-8
0 100 200 300 400 500 600 700 make of the detector. We use a continuous wave bat-
Δt(ns)
tery powered LED as a steady and controllable source
FIG. 3: g(2) Histograms for various detectors exhibit ofbackgroundilluminationinadditiontotheattenuated
distinct afterpulse behavior (each afterpulse peak is laser pulses (see Figure 1). We then measured the g(2)
marked by an arrow). For example, the τ-SPAD-fast histograms for different background count rates.
displays an unusually gradual decay while the
SPCM-NIR is the only detector make to exhibit higher
order afterpulses . The inset shows the higher order
Detector α α α
avg min max
afterpulses occurring at intervals equal to the dead time.
SPCM-NIR 3.97 ± 0.06 3.86 ± 0.05 4.06 ± 0.20
τ-SPAD-fast 3.31 ± 0.06 3.30 ± 0.07 3.32 ± 0.15
We verified that the higher order afterpulses seen are
TABLE II: The correction factor α to be applied for the
not the result of stray light, the shape of the laser pulse,
dead time depends on the make of detector. The table
electronic noise, impedance mismatch or optical reflec-
shows the average value (α ) as well as the minimum
tions. We also processed the data with different bin avg
(α ) and maximum (α ) values as the background
widths and laser pulse frequencies to ensure that the ob- min max
level was varied from 40kcps to 240kcps. The
served higher order afterpulse peaks are not due to digi-
SPCM-AQ4C is a fiber coupled detector and we could
tization noise.
not introduce background light using the LED in the
Further, we note that it is possible to explain the area
same manner as the other detectors and is hence
of the nth higher order peak based on the probability of
omitted from this table.
the first afterpulse (P(AP)) as P(AP)(n+1)+ the proba-
6
Figure 4a shows these histograms for the SPCM-NIR variation.
while Figure 4b shows the same for the τ-SPAD-fast Further, the total afterpulsing probability for several
modules21. We observe that the rate of accidental co- individual detectors all of the same manufacturer, part
incidences (racc) between the trigger signal and the at- number,andwithconsecutiveserialnumbersvarieddras-
tenuated laser pulse vary linearly with the background tically(insomecasesbetween5.1and8.5%)impliesthat
count rate in the dead time region. We also note that everyindividualdetectorneedstobecalibratedforallap-
the number of accidentals per bin in a region (cid:28) 0.7µs plicationsthatneedtoaccuratelymeasurecountratesor
awayfromthedetectioneventisproportionaltothenum- arrival times of photons.
ber of accidentals per bin during the dead time. We call
For many years, afterpulsing has been extensively
this proportionality constant α.
studied from a semiconductor physics based perspec-
Intheregionsbeforethedetectionevent,wellafterthe tive,whereitisimportanttounderstandinghowtrapped
detection event and even during the afterpulse, the mea- charges/energy levels decay. However, to correctly study
sured accidental corrections agreed with the value cal- this, one must separate the effects due to the behaviour
culated assuming Poissonian statistics. However, during of the diode or seimiconductor junction from the effects
the dead time we found that a correction of racc needed due to the electronics and quenching circuits. For ex-
α
to be applied by subtraction. Table II shows α for dif- ample, based on modeling the semiconductor junction, a
ferent detector makes. longer dead time is thought to lead to a lower afterpuls-
ing probability7. However, as seen in Table I and Fig-
ure 3 both the SPCM-AQ4C and the τ-SPAD-fast have
IV. CONCLUSION asignificantlylongerdeadtimethantheSPCM-NIRbut
the former has a lower afterpulse probability while the
We have clearly demonstrated that statistically sig- latter has a larger one. In this case it is impossible to
nificant different models are required to appropriately draw a conclusion about the relationship between dead
describe the distribution of electrical signals generated time and afterpulse probability without carefully consid-
by different brands/makes of detectors. This explains ering the quenching circuits used. This type of analysis
the conflicting nature of several previous studies; for ex- requires proprietary and confidential information about
ample14,15,23 show strong evidence for the power model the diode and circuits used by the manufacturer; which
while3,8 show equally compelling evidence for the mul- is inaccessible to a typical end-user. Instead of draw-
tiple exponential model and13 provides evidence for the ing potentially erroneous conclusions about semiconduc-
hyperbolic sinc model. Recently27 showed that the af- tor behavior based on which model had a better fit, we
terpulse probability is dependent on past events — a focus on an application oriented perspective. For most
propertynotconsideredintheexponential,power,orhy- practical purposes, it is sufficient to understand the sta-
perbolic sinc models. By comparing previously reported tistical nature of the afterpulses rather than their causal
results to our own, we realize that there is a large vari- mechanisms.
ation between the different manufactures and makes of We also would like to mention, that we do not con-
detectorscommonlyused. Thesuppressionofafterpulses sider a possible aging effect of the detectors. All mea-
bydifferentquenchingmethods20 leadsustobelievethat surementswereperformedinthetimespanofonlyafew
the afterpulsing behavior is more dependent on the elec- months. Commercial products, may have to be charac-
tronic quenching circuit used rather than the presence terizedrepeatedlyduringtheirlongoperationallifetimes.
anddistributionofdiscrete/continuous/quasi-continuous Thestudyofanyagingeffectsonthestatisticalbehaviour
deep levels. This clearly proves that none of the current ofAPD’singeneralisanintrestingavenueforfurtherex-
theoretical models are universal which makes it hard to ploration.
drawconclusionsabouttheunderlyingmechanismbased Most applications of APDs are hindered by afterpuls-
on fundamental semiconductor physics. ing, inmanycasestheseilleffectscanbecorrectedforin
We also report on the presence of higher order after- post-processing. However,todosoonemustcharacterize
pulsesinoneofthetesteddetectormodels. Tomakethis eachdetectorindividuallyasevidencedbythelargevari-
possible, unlike in several previous measurements7,13,25 ation in the afterpulse probabilities between detectors of
who used an auto-correlation signal, we use a cross- thesamemodelnumber,ageandmanufacturerunderal-
correlation histogram between the detector and the trig- most identical laboratory test conditions. It is possible,
ger. This allows us to look for both higher order af- although inadvisable, to ignore all clicks a few hundred
terpulses as well as the behavior during the dead time. ns after any detection event. This effectively increases
These higher order afterpulses can cause large errors in the dead time and avoids the bulk of afterpulses butthis
measurements of the arrival times of photons and must severely limits the maximum count rates and detection
be carefully accounted for. We were able to exclude efficiency due to saturation-like effects. To correctly ac-
frequency dependence in our detectors since we tested count for the ill effects of afterpulses it is sufficient to
all the results shown here for several different repetition characteriseeachindividualdetectorpriorto/duringuse,
rates(allfarfromdetectorsaturation)ofthelaserpulses using the method described in this work. Characteriza-
rangingfrom10kHzto1.2MHzandfoundnosignificant tionmethodsbasedonthetimingauto-correlationofde-
7
2×10-3
2×10-3 224000kkppccss 224000kkppccss
160kpcs 160kpcs
oincidence counts1×10-3 Coincidence counts120×××111000--330-40 -20 0 2C0orr4e0cte61d2840000kkkpppccc8sss0 100 oincidence counts1×10-3 Coincidence counts120×××111000--330 0 CΔot r(1rne0sc0)ted1284000kkkppp2cccsss00
C Δt (ns) C
0×100 0×100
-20 0 20 40 60 80 100 0 100 200
Δt(ns) Δt(ns)
(a) Excelitas SPCM-NIR APD module. (b) Laser Components τ-SPAD-fast APD module.
FIG. 4: g(2) Histograms for different background count levels, clearly showing the reduced detection efficiency in the
dead time region (between the large detection peak and time ∆t=0). We observe a linear scaling of the accidental
coincidences as we vary the background count rate. From which we determine a reduction factor α in this dead time
region (see Table II). Insets: The g(2) histograms corrected for background counts.
tectioneventscaneasilyoverlookfeaturessuchashigher 8A.C.Giudice,M.Ghioni,S.Cova,andF.Zappa. Aprocessand
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